Macroscopic Balances

Macroscopic Balances  List the assumptions given for a control volume and all of the conservation principles.

 What is a streamline? How is it used as an axis through the control volume?

 How do you calculate the average of a quantity over a surface?

Conservation of Mass  What is the name of the conservation of mass equation?

 Write down the version of the conservation of mass equation with only the assumption of steady state. What does this physically mean? What did these assumptions eliminate from the original equation?

 Write down the version of the conservation of mass equation with the assumptions of steady state, single fluid, and incompressible. What does this physically mean? What did these assumptions eliminate from the original equation?

Conservation of Energy  What are the three types of energy considered? Write the mathematical sum of the total energy.

 Write down the energy equation as first presented in class. What is assumed, and what does each term mean?

 Write down the engineering Bernoulli equation (5.34).

o What is assumed in this equation? What does each term mean? o What are the values of alpha at turbulent and laminar flow?

o How does it simplify for an isothermal ideal gas?

o How does it simplify for an incompressible fluid?

o What does it mean to write the engineering Bernoulli equation in the form of velocity heads?

o Where can we find the values for the losses?

Momentum Balance  Write the Momentum Conservation equation after all of the simplifying assumptions. List all of the assumptions.

o What is beta for turbulent and laminar pipe flow?

 What is the Bernoulli equation along a streamline? What was assumed in order to derive this equation?

Applications  What is a pitot tube? What assumptions can we make at different points? Where are good places to apply the Bernoulli equation?

 To find the force on a reducing bend, what assumptions are made to the continuity and conservation of energy equations?

 Refer to Figure 6-4 on page 111, a jet ejector. Describe how you could find one of the velocities given all other velocities and all areas. What equation would you use, and what assumptions would you make?

 Review the free jet (section 6.7) and the rotameter (section 6.8). What balances are performed, and what simplifying assumptions are made in each case?